a right triangle has a hypotenuse of length 16 and an angle of 45 degrees, with a side opposite this angle of length /sqrt2. a second right triangle also has an angle of 45 degrees and a side oppostie this angle with a length of 4\sqrt2. determind the length of the hypotenuse in the second triangle
From the first right triangle, we can use the sine ratio to find the length of the side adjacent to the angle of 45 degrees. Since the side opposite this angle has a length of √2, we have:
sin(45 degrees) = opposite/hypotenuse
sin(45 degrees) = √2/16
We can rearrange this equation to solve for the hypotenuse:
hypotenuse = √2 / sin(45 degrees) * 16
Using a calculator, we find:
hypotenuse ≈ 22.63
In the second right triangle, we are given the side opposite the angle of 45 degrees with a length of 4√2. Using the same sine ratio, we can find the hypotenuse:
hypotenuse = 4√2 / sin(45 degrees)
Using a calculator, we find:
hypotenuse ≈ 5.66
Therefore, the length of the hypotenuse in the second triangle is approximately 5.66.